5) A Runction f Cx) define sthe Fourier tronsformation asfollows:Î (w) = f (x) edx%3DSimilarly, the inverse Fourier tronsformation of a knownRunction ê lu) is found os :P(x) =f (x)%3DeBy loo king at this, find the Fourier tronsform of f (w)of the function given below and verifyfor a>0the shape of the function f(x) given to you by calculatingthe inverse fourier tronsform using the result you found- axex >0f Gx) =X

We are given a function: fx=e-ax x>00 x<0 We need to find the fourier transformation…

5) A function fCx) define s the Fourier tronsformation c R0llows: Î (w) = |f (x) e %3D Similarly, the inverse Fourier tronsformation of a knou Punction ê lw) is found os : P (x) = t f (w)e" dw %3D 2π

5) A function fCx) define s the Fourier tronsformation c R0llows: Î (w) = |f (x) e %3D Similarly, the inverse Fourier tronsformation of a knou Punction ê lw) is found os : P (x) = t f (w)e" dw %3D 2π

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

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Question

5) A Runction f Cx) define s
the Fourier tronsformation as
follows:
Î (w) = f (x) e
dx
%3D
Similarly, the inverse Fourier tronsformation of a known
Runction ê lu) is found os :
P(x) =
f (x)
%3D
e
By loo king at this, find the Fourier tronsform of f (w)
of the function given below and verify
for a>0
the shape of the function f(x) given to you by calculating
the inverse fourier tronsform using the result you found
- ax
e
x >0
f Gx) =
X <o

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